Problem: If $x \circledcirc y = 5y+3$ and $x \barwedge y = 4x^{2}-y^{2}$, find $(6 \barwedge -5) \circledcirc -1$.
Solution: We don't need to find $6 \barwedge -5$ because $x \circledcirc y$ depends only on the right operand. Find $x \circledcirc -1$ $ x \circledcirc -1 = (5)(-1)+3$ $ \hphantom{x \circledcirc -1} = -2$.